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The same process will now be carried out for a three-state HMM. There is little to modify
between the two, with the exception of modifying nstates = 3 and adjusting the plotting legend.
See Figure 14.7.
> # Fit a Hidden Markov Model with three states
> # to the S&P500 returns stream
> hmm <- depmix(returns ~ 1, family = gaussian(), nstates = 3,
data=data.frame(returns=returns))
> hmmfit <- fit(hmm, verbose = FALSE)
> post_probs <- posterior(hmmfit)
>
> # Plot the returns stream and the posterior
> # probabilities of the separate regimes
> layout(1:2)
> plot(returns, type=’l’, main=’Regime Detection’,
xlab=’’, ylab=’Returns’)
> matplot(post_probs[,-1], type=’l’,
main=’Regime Posterior Probabilities’,
ylab=’Probability’)
> legend(x=’bottomleft’, c(’Regime #1’,’Regime #2’, ’Regime #3’),
fill=1:3, bty=’n’)
Figure 14.7: Three-state Hidden Markov Model applied to S&P500 returns data
The length of data makes the posterior probabilities chart somewhat trickier to interpret.
Since the model is forced to consider three separate regimes it leads to a switching behaviour
between Regime #2 and Regime #3 in the calmer period of 2004-2007. However in the volatile
periods of 2008, 2010 and 2011, Regime #1 dominates the posterior probability indicating a